In the given figure, the arms of two angles are parallel.

If∠ABC = 70º, then find ∠DEF.

Given, The arms of two angles are parallel.

AB $\parallel$ DE

BC $\parallel$ EF

AB is parallel to DE. BC is a transversal. By using the property that when a pair of parallel lines are intersected by a transversal the pairs of corresponding angles are equal.

∠ABC = ∠DGC

∠DGC = ${70}^{\circ }$ (Given, ∠ABC = ${70}^{\circ }$)

BC is parallel to EF. DE is a transversal. By using the property that when a pair of parallel lines are intersected by a transversal the pairs of corresponding angles are equal.

∠DGC = ∠DEF

∠DEF = ${70}^{\circ }$

$\therefore$∠DEF = ∠DGC = ${70}^{\circ }$.